线性时不变系统Kalman标准分解中的几个问题

Some Questions on Kalman Standard Decomposition of Linear Time Invariable System

证明了线性时不变系统一般不能通过先可控分解,再分别对可控和不可控子系统进行可观分解而得到Kalman 标准型.并讨论了在4 个子空间< A｜β> ∩η、< A｜ β> ∩η⊥、< A｜ β> ⊥∩η和< A｜ β> ⊥∩η⊥中取一组基,构造一个化系统为Kalman 标准型的非奇异变换的可能性.最后,证明了在一定条件下存在一个正交变换,可将线性时不变系统化为Kalman

It is shown that for a linear time invariable system,its Kalman canonical form can not be obtained by decomposing the system into its controllable canonical form,and then decomposing its controllable and uncontrollable subsystems into their observable canonical form,respectively.The possibility is discussed to construct a non singular transformation which transforms the system to its Kalman canonical form through choosing a basis in <A|β>∩η,<A|β>∩η ⊥,<A|β> ⊥∩η and <A|β> ⊥∩η ⊥.Finally ,it is proved that the system can be transformed to its Kalman canonical form using an orthogonal transformation under appropriate conditions.